Newsgroups: comp.ai.fuzzy
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!oitnews.harvard.edu!purdue!lerc.nasa.gov!magnus.acs.ohio-state.edu!math.ohio-state.edu!howland.reston.ans.net!newsfeed.internetmci.com!news.mathworks.com!uunet!inXS.uu.net!news.interpath.net!sas!newshost.unx.sas.com!saswss
From: saswss@hotellng.unx.sas.com (Warren Sarle)
Subject: Re: fuzzy logic and probability
Originator: saswss@hotellng.unx.sas.com
Sender: news@unx.sas.com (Noter of Newsworthy Events)
Message-ID: <DurGs7.Ft7@unx.sas.com>
Date: Thu, 18 Jul 1996 22:50:31 GMT
X-Nntp-Posting-Host: hotellng.unx.sas.com
References: <4rfsju$pmb@ns1.nl.cis.philips.com> <31ED9CE7.25B7@hal-pc.org> <31EDB9C6.565D@hal-pc.org>
Organization: SAS Institute Inc.
Lines: 33


In article <31EDB9C6.565D@hal-pc.org>, "Michael D. Kersey" <mdkersey@hal-pc.org> writes:
|> ...
|> A membership function for say, the variable "height", could be formulated in the
|> following manner:
|>      1) Define or select from the language a set of labels, say the set
|>      { short, medium, tall },
|>      2) Using these terms, poll a sample of persons, asking them to
|>      classify other persons of measured height as being short, medium, or tall.
|>      From this we could infer the probabilities p(x,h) that a person of a given height
|>      h be classified as x = {short, medium, or tall} by someone from the general
|>      population of persons.
|>      3) Plot p(tall, h). It may not be a monotonically increasing function of height,
|>      ( e.g., perhaps wider persons are perceived as being less "tall", and we got
|>      a sample including a significant number of wide persons in one height range ).
|> 
|> Now p(x,h) are probability functions, but can also be used as membership functions. 

p(x|h) is a probability function.
p(h|x) is a likelihood function or a regression function.

|> To me, the most significant thing about fuzzy logic is not that it is associated
|> with probability in any particular way, but that it captures and renders explicit
|> ordinal information sometimes overlooked in qualitative models. In this way, it
|> promotes data from a so-called "nominal" scale to an "ordinal" scale. 

In the example above, you are _demoting_ interval data (h) to ordinal data (x).

-- 

Warren S. Sarle       SAS Institute Inc.   The opinions expressed here
saswss@unx.sas.com    SAS Campus Drive     are mine and not necessarily
(919) 677-8000        Cary, NC 27513, USA  those of SAS Institute.
